Interferometric techniques are commonly used to measure the profile of a surface of an object. To do so, an interferometer combines a measurement wavefront reflected from the surface of interest with a reference wavefront reflected from a reference surface to produce an interferogram. Fringes in the interferogram are indicative of spatial variations between the surface of interest and the reference surface.
A scanning interferometer scans the optical path length difference (OPD) between the reference and measurement legs of the interferometer over a range comparable to, or larger than, the coherence length of the interfering wavefronts, to produce a scanning interferometry signal for each camera pixel (herein also referred to as an interference signal) used to measure the interferogram. A limited coherence length can be produced, for example, by using a white-light source, which is referred to as scanning white light interferometry (SWLI). An interference signal is typically characterized by a sinusoidal carrier modulation (referred to as interference fringes). For SWLI, the sinusoidal carrier modulation is typically modified by a bell-shaped fringe-contrast envelope. In general, a SWLI-signal has a few fringes, modulated by the bell-shaped envelope, localized near the zero optical path length difference (OPD) position. The conventional idea underlying SWLI metrology is to make use of the localization of the fringes to measure surface profiles.
SWLI processing techniques include two principle trends. The first approach is to locate the peak or center of the envelope, assuming that this position corresponds to the zero optical path length difference of a two-beam interferometer for which one beam reflects from the object surface. The second approach is to transform the signal into the frequency domain and calculate the rate of change of phase with wavelength, assuming that an essentially linear slope is directly proportional to object position. See, for example, U.S. Pat. No. 5,398,113 to Peter de Groot. This latter approach is referred to as Frequency Domain Analysis (FDA).
Scanning interferometry can be used to measure surface topography and/or other characteristics of objects having complex surface structures, such as thin film(s), discrete structures of dissimilar materials, or discrete structures that are under-resolved by the optical resolution of an interference microscope. Such measurements are relevant to the characterization of flat panel display components, semiconductor wafer metrology, and in-situ thin film and dissimilar materials analysis. See, e.g., U.S. Patent Publication No. US-2004-0189999-A1 by Peter de Groot et al. entitled “Profiling Complex Surface Structures Using Scanning Interferometry” and published on Sep. 30, 2004, the contents of which are incorporated herein by reference, and U.S. Pat. No. 7,139,081 by Peter de Groot entitled “Interferometry Method for Ellipsometry, Reflectometry, and Scatterometry Measurements, Including Characterization of Thin Film Structures” and issued on Nov. 21, 2006, the contents of which are incorporated herein by reference.
Other techniques for optically determining information about an object include ellipsometry and reflectometry. Ellipsometry determines complex reflectivity of a surface when illuminated at an oblique angle (e.g., 60°) sometimes with a variable angle or with multiple wavelengths. To achieve greater resolution than is readily achievable in a conventional ellipsometer, microellipsometers measure phase and/or intensity distributions in the back focal plane of the objective, also known as the pupil plane, where the various illumination angles are mapped into field positions. Such devices are modernizations of traditional polarization microscopes or “conoscopes,” linked historically to crystallography and mineralogy, which employ crossed polarizers and a Bertrand lens to analyze the pupil plane birefringent materials.
Conventional techniques used for surface characterization (e.g., ellipsometry and reflectometry) rely on the fact that the complex reflectivity of an unknown optical interface depends both on its intrinsic characteristics (material properties and thickness of individual layers) and on three properties of the light that is used for measuring the reflectivity: wavelength, angle of incidence, and polarization state. In practice, characterization instruments record reflectivity fluctuations resulting from varying these parameters over known ranges.
Optimization procedures such as least-squares fits are then used to get estimates for the unknown parameters by minimizing the difference between measured reflectivity data and a reflectivity function derived from a model of the optical structure. These derived candidate solutions are often calculated in advance and stored in a library, which is searched to determine the correct solution by a least-squares or equivalent matching and interpolation technique. See, for example, K. P. Bishop et al. “Grating line shape characterization using scatterometry,” SPIE 1545, 64-73 (1991) and C. J. Raymond et al., “Scatterometry for CD measurements of etched structures,” SPIE 2725, 720-728 (1996).
Detailed modeling such as Rigorous Coupled Wave Analysis solves the inverse problem of discovering the feature structure that generates the observed interference signal observed diffraction effects. See, for example, reference of M. G. Moharam and T. K. Gaylord “Rigorous coupled-wave analysis of planar-grating diffraction,” JOSA, 71(7), 811 (1981) and S. S. H. Naqvi et al., “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt., 31(10), 1377-1384 (1992).
Analysis of the diffraction patterns from grating test patterns on masks and wafers provides non-contact measurements of linewidth and other feature characteristics associated with process control. See, for example, H. P. Kleinknecht et al., “Linewidth measurement on IC masks and wafers by grating test patterns,” Appl Opt. 19(4), 525-533 (1980) and C. J. Raymond, “Scatterometry for Semiconductor Metrology,” in Handbook of silicon semiconductor metrology, A. J. Deibold, Ed., Marcel Dekker, Inc., New York, 2001).